4.11 The Bootstrap Method (continued To calculate the 1.5 year rate we solve 4e0105+4e0104×10+104ek×15=96 to get R=0.1068or10.68% Similarly the two-year rate is 10.81% (see the equation on page 91) Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
4.11 Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University The Bootstrap Method （continued） • To calculate the 1.5 year rate we solve to get R = 0.1068 or 10.68% • Similarly the two-year rate is 10.81% （see the equation on page 91） 4 4 104 96 0 1047 0 5 0 1054 1 0 1 5 e e e − − −R + + = . . . .
4.12 Zero curve calculated from the data(Figure 4.1, page 92) 12 Zero Rate(%o 10.681 10.808 10.469 10.536 10 10.127 turity (yrs) 9 0.5 5 2.5 Options, Futures, and other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, 2003, Shanghai Normal University
4.12 Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University Zero Curve Calculated from the Data (Figure 4.1, page 92) 9 10 11 12 0 0.5 1 1.5 2 2.5 Zero Rate (%) Maturity (yrs) 10.127 10.469 10.536 10.681 10.808
4.13 Forward rates (远期利率) The forward rate is the future zero rate implied by todays term structure(期限结 构) of interest rates It is determined by the current zero rates The forward rate is for a specified future time period Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
4.13 Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University Forward Rates (远期利率) • The forward rate is the future zero rate implied by today’s term structure(期限结 构) of interest rates • It is determined by the current zero rates • The forward rate is for a specified future time period
4.14 Calculation of forward rates Table 4.4, page 93 Zero rate for forward rate an n-year Investment for n th Year Year(n) ( %per annum) ( %per annum 10.0 10.5 11.0 3 10.8 11.4 11.0 11.6 5 11.5 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
4.14 Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University Calculation of Forward Rates Table 4.4, page 93 Zero Rate for Forward Rate an n -year Investment for n th Year Year (n ) (% per annum) (% per annum) 1 10.0 2 10.5 11.0 3 10.8 11.4 4 11.0 11.6 5 11.1 11.5